Find the Value Using the Unit Circle sec((3pi)/2)

Problem

sec((3*π)/2)

Solution

1. Identify the definition of the secant function in terms of the unit circle coordinates (x,y)

sec(θ)=1/x

2. Determine the coordinates on the unit circle for the angle θ=(3*π)/2

(x,y)=(0,−1)

3. Substitute the xcoordinate into the secant formula.

sec((3*π)/2)=1/0

4. Evaluate the expression, noting that division by zero is undefined.

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Final Answer

sec((3*π)/2)=undefined

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